Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

12 questions

SA-4024-CG4-0012 marksL1 FoundationNon-calculatorTangents

A tangent to a curve at

P

passes through

(1,2)

and

(3,10)

. Estimate the gradient of the curve at

P

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0021 markL1 FoundationCalculatorTangents

On a distance–time graph, the gradient of the tangent at a point gives

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0031 markL1 FoundationCalculatorTangents

On a speed–time graph, the gradient of the tangent at a point gives

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0072 marksL1 FoundationNon-calculatorGraphical solutions

The graphs of

y=x^2

and

y=x+2

are drawn. Find the positive

x

-coordinate where they cross.

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0101 markL1 FoundationNon-calculatorGraphical solutions

Using the graph of

y=x^2+4

, write down how many solutions

x^2+4=0

has.

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0121 markL1 FoundationCalculatorTangents

At a maximum point of a curve, the gradient of the tangent is

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0042 marksL2 StandardNon-calculatorTangents

The tangent to

y=x^2

(3,9)

also passes through

(1,-3)

. Find the gradient of the curve at

(3,9)

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0052 marksL2 StandardNon-calculatorTangents

A tangent is drawn to a curve at

(2,5)

. The tangent crosses the

y

-axis at

(0,1)

. Find the gradient of the curve at

(2,5)

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0062 marksL2 StandardNon-calculatorGraphical solutions

The graph of

y=x^2-2x-3

is drawn. To solve

x^2-3x-1=0

, the line

y=x+c

is drawn. Find

c

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0082 marksL2 StandardCalculatorGraphical solutions

Use the graphs of

y=2^x

and

y=5

to estimate the solution of

2^x=5

, to 2 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0092 marksL2 StandardNon-calculatorGraphical solutions

The curve

y=x^3-3x

has a maximum at

(-1,2)

and a minimum at

(1,-2)

. How many solutions does

x^3-3x=1

have?

Salam Academy Original Practice · Proposed mark scheme

SA-4024-CG4-0112 marksL3 ExamNon-calculatorGraphical solutions

The graphs of

y=\dfrac1x

and

y=x

are drawn. Find the positive

x

-coordinate where they cross, and state how many crossing points there are altogether.

Salam Academy Original Practice · Proposed mark scheme